Judge Charles Breyer of the U.S. District Court in San Francisco approved the sweeping agreement between consumers, the U.S. government, California regulators and the German automaker in a written ruling a week after signaling he was likely to sign off.

He said the agreement is "fair, reasonable and adequate."

The settlement comes about a year after Volkswagen admitted that it rigged 11 million vehicles worldwide with software to dodge emissions standards.

The company is still facing criminal investigations by the U.S. Justice Department and German prosecutors. The U.S. probe could lead to additional financial penalties and criminal indictments.

About 475,000 Volkswagen owners in the U.S. can choose between a buyback or a free fix and compensation, if a repair becomes available.

Buybacks range in value from $12,475 to $44,176, including restitution payments. People who opt for a fix approved by the Environmental Protection Agency will receive payouts ranging from $5,100 to $9,852, depending on the book value of their car.

Volkswagen will also pay $2.7 billion for environmental mitigation and another $2 billion for clean-emissions infrastructure.

And the company has agreed to a $1.2 billion settlement with dealers over the same matter.

Meanwhile, VW is negotiating a separate settlement with more than 80,000 owners of 3-liter diesel vehicles fitted with similar software.

More than 336,000 of the eligible VW owners have already registered for the settlement, though they could back out if VW can't come up with a fix. The company has yet to receive approval from the Environmental Protection Agency, and if it fails to do so, everyone will be offered the buyback option.

VW plaintiffs attorney Elizabeth Cabraser told Judge Breyer last week that the deal "set a land speed record — probably an air speed record as well."

Fewer than 1% of eligible VW owners opted out of the deal before September deadline. People who did not respond are automatically considered to have taken the offer.

About two dozen VW owners objected to the deal during an Oct. 18 hearing. Most of the objections boiled down to complaints over the amount of the payout, while some critics also lambasted the automaker's "clean diesel" advertising and purposeful environmental pollution.

Mark Dietrich of San Francisco said he and his wife purchased an Audi, a VW luxury brand affected by the scandal, in 2010 prior to the arrival of their first child.

"We drank up their marketing materials and their promises of clean diesel," he told Judge Breyer. "We got played the fool."

VW attorney Robert Giuffra told the judge the deal "may well be one of the biggest settlements in consumer history" and represents VW's concerted attempt to make things right.

"Under any circumstance this is a fair and reasonable settlement for consumers," he said.